# Question 39

Challenge question #39 (05/12/2016)

Junior Question

A motorist, after having his car overhauled, finds that he can travel an additional $5$ km per litre of petrol. He is now using $2$ litres less for a journey of $200$ km than previously.

How many km per litre was he getting previously?

Suppose $a+b=1$ and $a^{2}+b^{2}=3$.
Find the value of $a^{5}+b^{5}$.